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A203621 Highly anti-imperfect numbers: n sets a record for the value of |sigma*(n)-n|, where sigma*(n) is the sum of the anti-divisors of n. 1
1, 2, 7, 10, 13, 17, 22, 27, 28, 32, 38, 45, 52, 60, 63, 67, 77, 95, 105, 130, 137, 143, 157, 158, 175, 193, 203, 247, 297, 315, 357, 423, 462, 472, 473, 578, 675, 682, 742, 770, 787, 1012, 1138, 1215, 1417, 1463, 1732, 1957, 2047, 2048, 2327, 2363, 2632 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Anti-imperfect numbers are anti-deficient numbers or anti-abundant numbers.

REFERENCES

n=1. Anti-divisors: 0. |0-1|=1

n=2. Anti-divisors: 0. |0-2|=2

n=3. Anti-divisors: 2. |2-3|=1 less than 2: 3 is not in the sequence.

n=4. Anti-divisors: 3. |3-4|=1 less than 2: 4 is not in the sequence.

n=5. Anti-divisors: 2,3. |5-3|=2 equal to the maximum: 5 is not in the sequence.

n=6. Anti-divisors: 4. |4-6|=2 equal to the maximum: 6 is not in the sequence.

n=7. Anti-divisors: 2,3,5. |10-7|=3 new maximum: 7 is in the sequence.

LINKS

Paolo P. Lava, Table of n, a(n) for n = 1..100

MAPLE

P:=proc(i)

local a, k, n, s;

s:=0;

for n from 1 to i do

  a:=0;

  for k from 2 to n-1 do if abs((n mod k)- k/2)<1 then a:=a+k; fi; od;

  if abs(n-a)>s then s:=abs(n-a); print(n); fi;

od;

end:

P(3000);

CROSSREFS

Cf. A066417, A074918, A192267, A192268.

Sequence in context: A277551 A029904 A026364 * A297832 A003158 A130336

Adjacent sequences:  A203618 A203619 A203620 * A203622 A203623 A203624

KEYWORD

nonn

AUTHOR

Paolo P. Lava, Jan 04 2012

STATUS

approved

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Last modified December 2 23:30 EST 2021. Contains 349445 sequences. (Running on oeis4.)